maxCPTParam: Find optimal parameters of a Pnode.NeticaNode to match...

In ralmond/PNetica: Parameterized Bayesian Networks Netica Interface

Find optimal parameters of a Pnode.NeticaNode to match expected tables

Description

These function assumes that an expected count contingency table can be built from the network; i.e., that LearnCPTs has been recently called. They then try to find the set of parameters maximizes the probability of the expected contingency table with repeated calls to mapDPC. This describes the method for maxCPTParam when the Pnode is a NeticaNode.

Usage

## S4 method for signature 'NeticaNode'
maxCPTParam(node, Mstepit = 5, tol = sqrt(.Machine$double.eps))

Arguments

node	A Pnode object giving the parameterized node.
Mstepit	A numeric scalar giving the number of maximization steps to take. Note that the maximization does not need to be run to convergence.
tol	A numeric scalar giving the stopping tolerance for the maximizer.

Details

This method is called on on a Pnode.NeticaNode object during the M-step of the EM algorithm (see GEMfit and maxAllTableParams for details). Its purpose is to extract the expected contingency table from Netica and pass it along to mapDPC.

When doing EM learning with Netica, the resulting conditional probability table (CPT) is the mean of the Dirichlet posterior. Going from the mean to the parameter requires multiplying the CPT by row counts for the number of virtual observations. In Netica, these are call NodeExperience. Thus, the expected counts are calculated with this expression: sweep(node[[]], 1, NodeExperience(node), "*").

What remains is to take the table of expected counts and feed it into mapDPC and then take the output of that routine and update the parameters.

The parameters Mstepit and tol are passed to mapDPC to control the gradient decent algorithm used for maximization. Note that for a generalized EM algorithm, the M-step does not need to be run to convergence, a couple of iterations are sufficient. The value of Mstepit may influence the speed of convergence, so the optimal value may vary by application. The tolerance is largely irrelevant (if Mstepit is small) as the outer EM algorithm does the tolerance test.

Value

The expression maxCPTParam(node) returns node invisibly. As a side effect the PnodeLnAlphas and PnodeBetas fields of node (or all nodes in PnetPnodes(net)) are updated to better fit the expected tables.

Author(s)

Russell Almond

References

Almond, R. G. (2015) An IRT-based Parameterization for Conditional Probability Tables. Paper presented at the 2015 Bayesian Application Workshop at the Uncertainty in Artificial Intelligence Conference.

See Also

Pnode, Pnode.NeticaNode, GEMfit, maxAllTableParams mapDPC

Examples

## This method is mostly a wrapper for CPTtools::mapDPC
getMethod(maxCPTParam,"NeticaNode")


sess <- NeticaSession()
startSession(sess)

irt10.base <- ReadNetworks(system.file("testnets","IRT10.2PL.base.dne",
                           package="PNetica"),
                           session=sess)
irt10.base <- as.Pnet(irt10.base)  ## Flag as Pnet, fields already set.
irt10.theta <- NetworkFindNode(irt10.base,"theta")
irt10.items <- PnetPnodes(irt10.base)
## Flag items as Pnodes
for (i in 1:length(irt10.items)) {
  irt10.items[[i]] <- as.Pnode(irt10.items[[i]])
  ## Add node to list of observed nodes
  PnodeLabels(irt10.items[[1]]) <-
     union(PnodeLabels(irt10.items[[1]]),"onodes")
}

casepath <- system.file("testdat","IRT10.2PL.200.items.cas",
                        package="PNetica")



BuildAllTables(irt10.base)
PnetCompile(irt10.base) ## Netica requirement

item1 <- irt10.items[[1]]
priB <- PnodeBetas(item1)
priA <- PnodeAlphas(item1)
priCPT <- PnodeProbs(item1)

gemout <- GEMfit(irt10.base,casepath,trace=TRUE)

calcExpTables(irt10.base,casepath)

maxAllTableParams(irt10.base)

postB <- PnodeBetas(item1)
postA <- PnodeAlphas(item1)
BuildTable(item1)
postCPT <- PnodeProbs(item1)

## Posterior should be different
stopifnot(
  postB != priB, postA != priA
)


DeleteNetwork(irt10.base)
stopSession(sess)

ralmond/PNetica documentation built on Sept. 19, 2023, 8:27 a.m.